How old are Jurgis and Ona at the beginning of The Jungle?
At the beginning of The Jungle, Ona is not yet sixteen years old. Jurgis, by contrast, is quite a bit older. It appears that he is about 26 years old.
We can see Ona's age in the very first pages of the book. At the beginning of the book, she is getting married. We are told that she is only 15 at that point. We can see this in the following quote:
She was so young—not quite sixteen—and small for her age, a mere child...
We know that Jurgis is quite a bit older than Ona is. In Chapter 7, when Jurgis' father dies, we are told
For twenty-five years old Antanas Rudkus and his son had dwelt in the forest together, and it was hard to part in this way...
Since the book starts with the family already in Chicago, that means that Jurgis was about 26 by the time the book starts.